Separately, the US State Department spokeswoman Heather Nauert said in a statement that Pompeo and Cavusoglu spoke to “discuss the case of Pastor Andrew Brunson”.
“The secretary and foreign minister committed to continued discussions to resolve the matter and address other issues of common concern,” Nauert added.
The conversation follows Thursday's phone call between Cavusoglu and Pompeo after Turkey responded to remarks made by US President Donald Trump when he threatened the country with sanctions unless Ankara released the detained American pastor.
In a move seen as an attempt to interfere with the judiciary of NATO-member Turkey, Trump tweeted: "The United States will impose large sanctions on Turkey for their longtime detainment of Pastor Andrew Brunson."
Turkish Foreign Minister Mevlut Cavusoglu had responded to the threat in a tweet: “No one dictates Turkey. We will never tolerate threats from anybody. Rule of law is for everyone; no exception.”
Brunson was moved from jail and placed under house arrest Wednesday after being detained in the Aegean province of Izmir in December 2016.
He was charged with spying for the PKK -- a designated terrorist group in the US and Turkey -- and the Fetullah Terrorist Organization (FETO), the group Turkey accuses of orchestrating the defeated July 2016 coup attempt.
Earlier on Saturday, Cavusoglu also spoke with his Saudi counterpart Adel al-Jubeir.
ANADOLU/MNA